if the number of squares formed from the chess board is 385 .find the dimensions of the chess board.
thanks in advance
thanks in advance
the answer is 10 by 10
Soln:
Let the Chess board be of dimension N by N.
No of 1 by 1 squares = N^2.
No of 2 by 2 squares = (N-1)^2
No of 3 by 3 squares= (N-2)^2
.
.
.
No of (N-1) by (N-1) squares = 2^2
No of N by N squares = 1^2
So,
total possiblesquares in a N BY N chess board = Sum of thesquares of first N ntural numbers.
=> N*(N+1)*(2N+1)/6 = 385
N=10.
Thanks,
Jaxis.
